Abstract
Quantum tomography is an important tool for the characterization of quantum operations. In this paper we present a framework of quantum tomography in fermionic systems. Compared with qubit systems, fermions obey the superselection rule, which sets constraints on states, processes, and measurements in a fermionic system. As a result, we can only partly reconstruct an operation that acts on a subset of fermion modes and the full reconstruction always requires at least one ancillary fermion mode in addition to the subset. We also report a protocol for the full reconstruction based on gates in a Majorana-fermion quantum computer, including a set of circuits for realizing the informationally complete state preparation and measurement.
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